Tag: oscillations and waves

Questions Related to oscillations and waves

In Young's double slit experiment, the phase difference between the two waves reaching at the location of the third dark fringe is  

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $\pi$

  2. $\cfrac{3\pi}{2}$

  3. $5 \pi$

  4. $3 \pi$

Show answer
Correct Option: C

In the above question, the intensity of the waves reaching a point P far away on the x-axis from each of the four sources is almost the same and equal to $I _0.$ Then,

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. If $d=\lambda /4,$ the intensity at P is $4I _0.$

  2. If $d=\lambda /6,$ the intensity at P is $3I _0.$

  3. If $d=\lambda /2,$ the intensity at P is $3I _0.$

  4. None of these is true

Show answer
Correct Option: B

The amount of light that falls per unit area held perpendicular to the rays in one second is called

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. Candle power

  2. Dioptre

  3. Lumen

  4. Intensity of illumination

Show answer
Correct Option: D
Explanation:

Candle power- It is the rating of light output at source. It is the the candle's luminous intensity in a particular direction.

Dioptre- It is the ability of a lens to bend the light rays. A unit of power of lens.
Lumen- The amount of energy emanating from one square meter of surface.
Intensity of illumination - The amount of light falling on per unit area, held perpendicular to the rays in one second.

The phase difference between two waves from successive half period zones or strips is :

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $\dfrac{\pi}{ 4}$

  2. $ \dfrac{\pi}{ 2}$

  3. $ \pi $

  4. zero

Show answer
Correct Option: C
Explanation:

The half period zone is provided by an optical device known as zone plate. It is simply a plane parallel gloss plate having concentric circles of radii accurately proportional to the square roots of the consecutive natural numbers 1,2,3 ... etc. The area is given by $\pi \gamma ^{2}$. Hence the
areas are $\pi , 2\pi , 3\pi , 4\pi$,---
The phase difference is thus $\pi$ between each successive half period zones of strips.

In Young's double slit experiment, the constant phase difference between two sources is $\dfrac{\pi }{2}$. The intensity at a point equidistant from the slits in terms of maximum intensity $I _{\circ}$ is :

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $I _{\circ}$

  2. $I _{\circ}/2$

  3. $3I _{\circ}/4$

  4. $3I _{\circ}$

Show answer
Correct Option: B
Explanation:

If there is no phase difference let
the Intensity equal to maximum Intensity be $I _{0}$
For a phase difference $\theta $ then
Intensity at a point equidistant from the two
slits is given by
$\dfrac{I _{0}}{2}(1+cos^{2}\theta )$
As $\theta =\pi /2$
we get $\dfrac{I _{0}}{2}(1+0)=\dfrac{I _{0}}{2}$
Thus Intensity $=\dfrac{I _{0}}{2}$

The maximum intensity produced by two coherent sources of intensity $I _{1}$ and $I _{2}$ constructively will be:

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $I _{I}+I _{2}$

  2. $I _{I}^{2}+I _{2}^{2}$

  3. $I _{I}+I _{2}+2\sqrt{I _{1}I _{2}}$

  4. zero

Show answer
Correct Option: C
Explanation:

If the angle between two coherent sources is $\theta $ then the Intensity after Interference is given by $I _{1}+I _{2}+2\sqrt{I _{1}I _{2}} cos \theta $. For constructive Interference $\theta =2n\pi $ Thus Intensity is $I _{1}+I _{2}+2\sqrt{I _{1}I _{2}}$

The intensity ratio for the two interfering beam of light is $\beta$. What is the value of 
$\dfrac{I _{max}-I _{min}}{I _{max}+I _{min}}$ ?

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. 2$\sqrt{\beta}$

  2. $\dfrac{2\sqrt{\beta}}{1+\beta}$

  3. $\dfrac{2}{1+\beta}$

  4. $\dfrac{1+\beta}{2\sqrt{\beta}}$

Show answer
Correct Option: B
Explanation:

Given $\cfrac { { I } _{ 1 } }{ { I } _{ 2 } } =\beta $

${ I } _{ max }={ I } _{ 1 }+{ I } _{ 2 }+2\sqrt { { I } _{ 1 }{ I } _{ 2 } } $
${ I } _{ min }={ I } _{ 1 }+{ I } _{ 2 }-2\sqrt { { I } _{ 1 }{ I } _{ 2 } } $
$\therefore \cfrac { { I } _{ max }-{ I } _{ min } }{ { I } _{ max }+{ I } _{ min } } \quad =\cfrac { 4\sqrt { { I } _{ 1 }{ I } _{ 2 } }  }{ 2({ I } _{ 1 }+{ I } _{ 2 }) } \quad =\frac { 2\sqrt { { I } _{ 2 }^{ 2 }\beta  }  }{ { I } _{ 2 }(\beta +1) } \quad =\cfrac { 2\sqrt { \beta  }  }{ \beta +1 } $

Let ${a _1}$ and ${a _2}$ be the amplitudes of two light waves of same frequency and ${\alpha _1}$ and ${\alpha _2}$ be their initial phases. The resultant amplitude due to the superposition of two light waves is

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $R = \sqrt {a _1^2 + a _2^2 + 2{a _1}{a _2}} $

  2. $R = {a _1} - {a _2}$

  3. $R = \sqrt {a _1^2 + a _2^2 + 2{a _1}{a _2}\cos \left( {{\alpha _1} - {\alpha _2}} \right)} $

  4. $R = \sqrt {a _1^2 + a _2^2 - 2{a _1}{a _2}} $

Show answer
Correct Option: C
Explanation:

The angle between two light waves $={ \alpha  } _{ 1 }-{ \alpha  } _{ 2 }$

Resultant $=\sqrt { { a } _{ 1 }^{ 2 }+{ a } _{ 2 }^{ 2 }+2{ a } _{ 1 }.{ a } _{ 2 }\cos { ({ \alpha  } _{ 1 }-{ \alpha  } _{ 2 }) }  } $

In the interference of waves from two sources of intensities $I _o$ and $4I _o$, the intensity at a point where the phase difference is $\pi$, is?

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $I _o$

  2. $2I _o$

  3. $3I _o$

  4. $4I _o$

Show answer
Correct Option: A
Explanation:

$I=I _1+I _2+2\sqrt{I _1I _2}\cos\theta =I _o+4I _o+2\sqrt{(I _o\times 4I _o)}\cos\pi =I _o$
Hence (A) is correct.

In Young's double slit experiment, when two light waves form third minimum, they have 

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. Phase difference of $3 \pi$

  2. Path difference of $3 \lambda $

  3. Phase difference of $\dfrac{5\pi}{2}$

  4. Path difference of $\dfrac{5\lambda }{2}$

Show answer
Correct Option: D
Explanation:

For minima , path difference=$\dfrac{(2n-1)\lambda}{2}$........(1)

          $n=3$
 so, putting in (1),
we get, path difference=$\dfrac{5\lambda}{2}$

Phase diffrence $\dfrac{\Delta\phi}{2 \pi}=\dfrac {\Delta X}{\lambda}$
 
$\Delta \phi =2\pi \dfrac {\Delta X}{\lambda} $

 $\Delta \phi =2\pi \dfrac {5 \lambda /2}{\lambda} =5 \pi$